Ask Emily is a biweekly column by Emily Bazar of the CHCF Center for Health Reporting, answering questions about the Affordable Care Act. Read all her columns atsacbee.com/askemily.

Obamacare’s inaugural open-enrollment period is over, and all you enrollees can breathe easy now.

Someday I’d like to write that sentence and mean it, but not today.

Instead, it’s time to take a look at an unwelcome surprise that is turning up in some of your new policies, whether you bought them through Covered California, the state’s health insurance exchange, or on the private market.

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Q: I learned today that the health “insurance” I purchased for my family through Covered California does not have ANY maximum out-of-pocket cost on out-of-network providers. … How is that even possible? Our family is now faced with potentially infinite costs that could wipe us out.

A: Let’s start with a quick refresher.

An out-of-pocket maximum is the most you would pay during the term of your health policy (usually one year) before your insurance begins paying 100 percent of covered medical services.

It wasn’t until recently that Burke realized that those much-publicized out-of-pocket maximums – including hers – only apply to services obtained from medical providers IN the plan’s network.

So what about providers who are not in network? Were limits set on those costs?

In her case, to her shock, no.

As it turns out, insurers get to decide the dollar limits – if any – for themselves.

“The out-of-network, out-of-pocket costs for each plan would be at the plans’ discretion,” says Covered California spokesman Roy Kennedy. “You would need to inquire with the individual plans on what their policy is for out-of-network costs.”

What’s the big deal, you may be wondering. Burke and others should just stay in their networks, right?

In this new health insurance environment, that’s easier said than done.

Insurers have created “narrow networks” for many of their new plans. In plain terms, that means they have whittled down the number of participating doctors and hospitals. The providers agree to charge insurers lower fees in return for higher volumes of patients.

But for consumers, staying in network has become more difficult because there are fewer providers serving more patients.

(Good luck confirming whether your doctor and hospital are in network. Misinformation and inaccuracies have plagued the network lists since the beginning.)

Burke poses a hypothetical: What if she needs surgery? She’ll make sure her doctor and hospital are in network. But, she notes, they won’t be the only ones providing services.

“One can’t know during surgery whether the assistant surgeon, the radiologist, the anesthesiologist, etc., are in network or not,” she says.

This doesn’t apply just to Covered California plans. Priscilla Myrick, also of Berkeley, bought an Anthem Blue Cross PPO ( Preferred Provider Organization) family plan on the private market.

Earlier this year, she visited the cardiologist she used to see through her previous Anthem plan and had a mammogram and bone density test at an imaging center that used to be in network.

Then she opened her mailbox and found bills totaling more than $1,500.

Myrick started digging. She learned that her cardiologist and imaging center are no longer in her network, which sent her bills skyrocketing.

Then she discovered that Anthem would assume all costs for covered services outside its network only after she had paid $30,000 out of her own pocket.

Myrick is a retired certified public accountant. “I know how to look at numbers,” she says.

But that one had not been apparent when she shopped around for plans. “How was anyone supposed to know this?” she asks.

Myrick has since canceled a follow-up procedure ordered by the cardiologist because “I couldn’t find out how much it was going to cost,” she says.

Darrel Ng, an Anthem spokesman, says out-of-pocket maximums for out-of-network providers range from $10,000 to $18,000 for the company’s individual plans and $20,000 to $36,000 for family plans on the private market. On Covered California, they range from $10,000 to $15,000 for individuals, he says, and from $20,000 to $30,000 for families.

He urges consumers to do their homework before getting care, if possible, to ensure their providers are in network.

“We would encourage them to contact the hospital and find out whether all the different parts of the medical system they’ll be touching are in their network and ask, if possible, that in-network providers be used,” Ng says.

Once again, easier said than done. How will the hospital know which radiologist or pathologist or fill-in-the-blank-ologist will be working at the time of your surgery one month from now?

“Who would answer those questions? The receptionist at the hospital?” Burke asks. “It’s impossible.”

I tend to agree.

Here’s my advice: Find out what your limit is for out-of-network providers.